How do you determine the constant of variation for the direct variation given -4y=8x+16?

1 Answer
Alan P.
Oct 21, 2015

-4y=8x+16 is not a direct variation

Explanation:

-4y=8x would be direct variation (with a constant of variation = (-2)
Doubling the value of x doubles the value of y
and the ratio y/x = -2
color(white)("XXXXXX"){: (x,color(white)("XXX"),y,color(white)("XXX"), y/x), (1,color(white)("XXX"),-2,color(white)("XXX"),-2), (2,color(white)("XXX"),-4,color(white)("XXX"),-2), (3,color(white)("XXX"),-6,color(white)("XXX"),-2), (4,color(white)("XXX"),-8,color(white)("XXX"),-2) :}

However
-4y=8x+16 is not a direct variation
color(white)("XXXXXX"){: (x,color(white)("XXX"),y,color(white)("XXX"), y/x), (1,color(white)("XXX"),-6,color(white)("XXX"),-6), (2,color(white)("XXX"),-8,color(white)("XXX"),-4), (3,color(white)("XXX"),-10,color(white)("XXX"),-3 1/3), (4,color(white)("XXX"),-12,color(white)("XXX"),-3) :}
Note that the ratio y/x is not a constant in this case!

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